1. Field of Invention
The present invention relates to string tensioning devices and methods for stringed musical instruments, such as guitars or the like.
2. Description of Related Art
Stringed musical instruments typically provide a fixed anchor on one end of each string and a mechanism on the other end which allows a user to establish a select amount of tension in the string. The frequency the string oscillates at depends on several parameters such as the vibrating length of the string, its tension, diameter, and material constants. Construction details, such as winding another string around the core string (often found on bass strings) may have also an effect, but mainly contribute to the harmonics content. As is known from physics, the relationship between oscillating frequency and string tension is not linear, but is proportional to the square root of the string tension.
The mechanism used to set the tension of the string is often referred to as the “tuning peg”, “tuning machine” or “machine head”. A simple embodiment is a tuning peg inserted into the appropriate part of the instrument, typically the neck in guitars, banjos and the like. An extension of the peg typically comprises a cylindrical post around which the string is wound a couple of turns. Rotating the peg rotates the post, which changes the string tension, and thereby changes the oscillating frequency and thus the tuning of the string.
To hold the tune there is first an interference fit of the peg with the body of the instrument. Second, there develops a friction force which resists the string tension back driving the peg. This friction force comes as the result of the string tension inducing a radial force on the peg, which in turn, via the friction coefficient applicable between the material of the peg and the material of the body of the instrument, creates a tangential force, which in turn counter balances the torque that comes as a result of the string tension acting on the radius of the post. Thus, in the absence of willful rotation of the peg, the string tension remains constant unless offsetting forces occur, which can de-tune the string oscillation. This, for instance, may come from age related shrinking of the material from which the instrument is constructed. Among the “offsetting forces” are aging of the instrument body material so that the friction fit loosens.
Another kind tuning mechanism is the tuning machine or machine head, which uses a gear mechanism or a worm gear arrangement, which, by design, provides a self jamming feature if a low pitch or high transmission ratio of the worm gear is implemented. These arrangements are well known in the art. A machine head with a worm gear arrangement is shown in FIG. 1, and typically comprises a tuning handle 2 secured to an end of a worm shaft 4 which extends through a machine head body 6. A worm wheel 8 is meshed with a worm 10 of the worm shaft 4 inside the body 6, and a cylindrical post 12 is connected to the worm wheel 8 and aligned with the rotational axis of the worm wheel 8. The cylindrical post 12 extends to the same side of the neck of the guitar as the strings, and is aligned such that its axis is perpendicular to the strings. In operation, as the tuning handle 2 (hence worm shaft 4) is rotated, it rotates the worm wheel 8, hence the cylindrical post 12. By this, a guitar string that is inserted through a guitar string insertion hole 14 defined in the cylindrical post, is wound or unwound on or from the cylindrical post 12, thereby the guitar string is allowed to be tuned.
In known stringed instruments and the prior art, the diameter of the cylindrical posts of the machine heads or tuning pegs onto which the strings are fastened and wound—and in the case of machine heads, the gear ratios—are the same for all strings used on a given instrument. As a result, the tuning sensitivity, or the amount of tonal change of the string per angular displacement of the cylindrical post, changes from string to string. For example, with some guitars equipped with prior art tuning apparatus having equal cylindrical post diameters (and gear ratios in the case of machine heads), a quarter turn on the tuning peg or tuning handle on the D-string of the guitar may result in a tonal shift of 8 semi-tones, whereas the same quarter turn of the tuning peg or tuning handle on the G-string may result in a tonal shift of 14 semi-tones. This example highlights the significant variance in tuning sensitivity between the strings that is intrinsic to the prior art tuning devices, such as tuning pegs and machine heads.
The variance in tuning sensitivity between the various strings on a stringed instrument can present a significant challenge for a performer in tuning his or her instrument, either before or during a performance, since the strings having a higher tuning sensitivity typically require more iterations of loosening and tightening of the string tension due to easily overshooting the target. Accordingly, it would be advantageous to have machine heads or tuning machines that are equipped to provide equal or substantially equal tuning sensitivity for the strings employed in an ensemble, i.e. on the same instrument.